The thermal conductivity of solid parahydrogen containing 0.2 to 5% orthohydrogen has been measured over the temperature range 1.5-6 \ifmmode^\circ\else\textdegree\fi{}K. On the low-temperature side of the conductivity maximum, the conductivity shows both a ${T}^{3}$ dependence and a strong dependence on orthohydrogen concentration. Within the resolution of the measurements, no (static) impurity scattering attributable to the orthohydrogen could be detected. We discuss the significance of these results in relation to a recent calculation that emphasizes the impurity scattering of phonons by orthohydrogen.